Scaling hair with the mesh
The easiest way would be to use Drivers.

Select your character, and, in the Properties panel, switch to the Particle System tab; At the top, there's a Hair Length field - press RMB (Right Click) and select Add Driver.

Now, switch to the Graph Editor (you could switch a Window to this, but it's easier, from the Default Screen Layout, to double press Ctrl + Left Arrow or to go to the Header and click besides "Default" and choose Animation), set type to Drivers, press N and select your driver from the left side. Select your objects name on the Obj field, then set the type to either X, Y or Z scale. set the Expression to be scale * var, where scale is the Hair Length and var is the variable you just setup.

Now, when you scale your object up, the hair will scale properly.